{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Volatility smile and model calibration\n",
    "\n",
    "\n",
    "## Contents\n",
    "   - [How to produce the smile?](#sec1)\n",
    "       - [Implied volatility](#sec1.1)\n",
    "       - [Lewis representation](#sec1.2)\n",
    "   - [Market data](#sec2)\n",
    "       - [1 week maturity](#sec2.1)\n",
    "       - [6 months maturity](#sec2.2)\n",
    "       \n",
    "       \n",
    "       \n",
    "In this notebook, we discuss in a very **basic and naive** way the implied volatility of options.\n",
    "\n",
    "The **Implied Volatility** is that value $\\sigma$ that must be inserted into the Black-Scholes (BS) formula in order to retrieve the option price quoted in the market:\n",
    "\n",
    "$$ BS\\;(S, K, T, r, \\sigma) = P  $$\n",
    "\n",
    "where $S$ is the underlying spot price, $K$ is the strike, $T$ time to maturity, $r$ risk free interest rate and $P$ the option price quoted in the market. All these quantities are **observable**.     \n",
    "The only **non observable** quantity is $\\sigma$.\n",
    "However, since BS is an increasing continuous function of $\\sigma$, there is a one-one correspondence \n",
    "\n",
    "$$\\sigma \\longleftrightarrow BS\\;(S, K, T, r, \\sigma)$$\n",
    "\n",
    "where all the other variables are kept fixed.    \n",
    "For this reasons, it is common to quote option market prices in terms of implied volatilities.\n",
    "\n",
    "According to the assumptions of the Black-Scholes model, the stock price follows a Geometric Brownian Motion and the implied volatility (IV) should be the same for all $K$, $T$. \n",
    "In practice, however, it depends on both. This relation $\\sigma(K, T)$ is called a **volatility surface**.    \n",
    "The dependence of IV on $T$ is called **term structure**, while the dependece on $K$ is called **volatility smile**.\n",
    "In this notebook I will consider only the volatility smile.\n",
    "\n",
    "But... why does the volatility change for different $K$ and $T$?        \n",
    "The sad truth is that the Geometric Brownian Motion is not a good model to describe the underlying dynamics!\n",
    "\n",
    "And here there are plenty of nice quotes to recall such as: \n",
    "\n",
    "> *\"Essentially, all models are wrong, but some are useful\".* [George Box](https://en.wikipedia.org/wiki/All_models_are_wrong)\n",
    "\n",
    "> *\"The implied volatility is the wrong number to put in the wrong formula to obtain the right price\".* Riccardo Rebonato [1]\n",
    "\n",
    "Some models (still wrong, but more useful) that better replicate the price dynamics, and under an appropriate risk neutral measure, are able to reproduce the volatility surface are:\n",
    "1. Local volatility models:  $ dS_t = \\mu S_t dt + S_t \\sigma(t, S_t) dW_t $. \n",
    "\n",
    "2. Stochastic volatility models, e.g. Heston model.\n",
    "\n",
    "3. Exponential or Geometric Lévy processes, e.g. Merton Jump-Diffusion model, NIG, Variance Gamma.\n",
    "\n",
    "4. Combination of stochastic volatility and jumps, e.g. [Bates model](https://en.wikipedia.org/wiki/Stochastic_volatility_jump). These type of models are the best for this purpose (see [2]). The reason is that they describe better the empirical features of the prices, such as volatility clustering and jumps. \n",
    "The presence of many parameters makes these models much more flexible.\n",
    "\n",
    "Here I consider only the case of stochastic volatility and Lévy processes, since I have already introduced them in the notebooks **1.4** and **1.5**.\n",
    "\n",
    "When considering complex models, it is very difficult to pass from the physical measure to the correct risk neutral measure (which is not unique).\n",
    "For this reason, the best approach is to derive the model parameters directly from the prices (usually European call and put options with different strikes and maturities) \n",
    "already quoted in the market.\n",
    "The process of choosing the risk neutral parameters for a model, such that it reproduces the prices in the market is called **model calibration**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from functions.Parameters import Option_param\n",
    "from functions.Processes import Diffusion_process, Merton_process, VG_process, Heston_process\n",
    "from functions.BS_pricer import BS_pricer\n",
    "from functions.Merton_pricer import Merton_pricer \n",
    "from functions.VG_pricer import VG_pricer\n",
    "from functions.Heston_pricer import Heston_pricer\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy as scp\n",
    "import scipy.stats as ss\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.optimize as scpo\n",
    "from functools import partial\n",
    "from itertools import compress\n",
    "import os\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec1'></a>\n",
    "# How to produce the smile?\n",
    "\n",
    "\n",
    "Alright... Let us check if the \"complex models\" mentioned above, are able to reproduce the volatility smile!\n",
    "\n",
    "In the following cell, I'm going to create the objects for the **Black-Scholes, Merton, Variance Gamma and Heston** pricers. I chose the values of the process parameters such that the processes have similar variance.    \n",
    "The option is a European call with strike $K=100$, and maturity $T=1$. We will see below that changing the time to maturity can create problems.\n",
    "\n",
    "The notation is the same I used in the other notebooks. If you have forgotten it, check the *doc*:    \n",
    "You can type `Heston_param.__doc__` or `Heston_param??` in a cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "T = 1\n",
    "S0 = 100; K = 100\n",
    "opt_param = Option_param(S0=S0, K=K, T=T, v0=0.04, exercise=\"European\", payoff=\"call\" )\n",
    "\n",
    "diff_param = Diffusion_process(r=0.1, sig=0.2)\n",
    "Merton_param = Merton_process(r=0.1, sig=0.1, lam=0.8, muJ=-0.04, sigJ=0.2)\n",
    "VG_param = VG_process(r=0.1, theta=-0.09, sigma=0.19, kappa=0.6)\n",
    "Heston_param = Heston_process(mu=0.1, rho=-0.3, sigma=0.6, theta=0.04, kappa=5)\n",
    "\n",
    "BS = BS_pricer(opt_param, diff_param)\n",
    "VG = VG_pricer(opt_param, VG_param)\n",
    "Mert = Merton_pricer(opt_param, Merton_param)\n",
    "Hest = Heston_pricer(opt_param, Heston_param)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us create a grid of strikes $[50, 55, ..., 145, 150]$, and compute the option prices.    \n",
    "In this case, the best approach is to use the Fourier Transform method described in the notebook **1.4**.     \n",
    "**This method is super fast!!**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "strikes = np.arange(50,151,5)    # strike grid\n",
    "BS_prices = BS.FFT(strikes)\n",
    "Mert_prices = Mert.FFT(strikes)\n",
    "Hest_prices = Hest.FFT(strikes)\n",
    "VG_prices = VG.FFT(strikes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Well... if there is a closed formula, why not use it?   \n",
    "\n",
    "The closed formula is always the best solution, but the FFT method is very fast and has a small error. You won't notice the difference.\n",
    "\n",
    "For VG and Heston there is no closed formula. A possible alternative is to use the Fourier inversion method. \n",
    "\n",
    "Let's see how small is the error:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Closed formula prices\n",
    "BS_prices_cl = np.zeros_like(strikes, dtype=float)\n",
    "VG_prices_cl = np.zeros_like(strikes, dtype=float)\n",
    "Mert_prices_cl = np.zeros_like(strikes, dtype=float)\n",
    "Hest_prices_cl = np.zeros_like(strikes, dtype=float)\n",
    "\n",
    "for i,K in enumerate(strikes):\n",
    "    BS.K = K; VG.K = K; Mert.K = K; Hest.K = K\n",
    "    BS_prices_cl[i] = BS.closed_formula()  \n",
    "    VG_prices_cl[i] = VG.Fourier_inversion()  \n",
    "    Mert_prices_cl[i] = Mert.closed_formula() \n",
    "    Hest_prices_cl[i] = Hest.Fourier_inversion() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Closed vs FFT. Total absolute error BS:  1.2537768903086999e-06\n",
      "Closed vs FFT. Total absolute error VG:  3.1493056313891543e-06\n",
      "Closed vs FFT. Total absolute error Merton:  3.2961514538909498e-06\n",
      "Closed vs FFT. Total absolute error Heston:  2.103745847747973e-06\n"
     ]
    }
   ],
   "source": [
    "print(\"Closed vs FFT. Total absolute error BS: \", np.linalg.norm(BS_prices-BS_prices_cl,1) )\n",
    "print(\"Closed vs FFT. Total absolute error VG: \", np.linalg.norm(VG_prices-VG_prices_cl,1) )\n",
    "print(\"Closed vs FFT. Total absolute error Merton: \", np.linalg.norm(Mert_prices-Mert_prices_cl,1) )\n",
    "print(\"Closed vs FFT. Total absolute error Heston: \", np.linalg.norm(Hest_prices-Hest_prices_cl,1) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Indeed... very small!\n",
    "\n",
    "#### Comments:\n",
    "\n",
    "At short maturities e.g. $T=0.01$, the Fourier inversion method may have problems. In our case it may have problems for the VG and Heston model. The reason is that the numerical integration used in the Fourier inversion method has ad-hoc bounds for the truncation of the integral. \n",
    "Usually, for small values of $T$, the tails of the integrand decay very slowly and the ad-hoc bounds produce a truncation error. \n",
    "\n",
    "Similar problems happen also for other numerical methods.    \n",
    "In general, there are always problems in pricing deep OTM (out of the money) options for very short maturities, when the closed formula is not available. \n",
    "The reason is that the error of the numerical method is usually bigger than the option price itself!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec1.1'></a>\n",
    "## Implied volatility\n",
    "\n",
    "How to find the value $\\sigma$ such that  \n",
    "\n",
    "$$ BS\\;(S, K, T, r, \\sigma) - P = 0 $$\n",
    "\n",
    "for fixed $S, K, T, r$ ?\n",
    "\n",
    "We have to use numerical methods!\n",
    "\n",
    "The most common methods are the [Newton](https://en.wikipedia.org/wiki/Newton%27s_method) method and the [Bisection](https://en.wikipedia.org/wiki/Bisection_method) method. A more advanced method is the [Brent](https://en.wikipedia.org/wiki/Brent%27s_method) method.    \n",
    "Of course all of them are implemented in `scipy.optimize`: \n",
    "[Newton](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.newton.html#scipy.optimize.newton), \n",
    "[Bisection](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.bisect.html#scipy.optimize.bisect), [Brent](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.brentq.html#scipy.optimize.brentq).    \n",
    "\n",
    "At first sight, the Newton method seems quite good since the derivative of BS with respect to $\\sigma$ is known analytically:\n",
    "\n",
    "$$ \\text{VEGA:} \\quad \\frac{\\partial BS}{\\partial \\sigma} = S \\sqrt{T} N'(d_1) $$\n",
    "\n",
    "where N'(x) is the standard normal density and $d_1$ is a variable defined...everywhere :) (see notebook **1.1**).     \n",
    "The Newton method has quadratic convergence if some conditions are satisfied.\n",
    "However, for high values of $\\sigma$ the VEGA can be very close to zero, and this makes the convergence slow.   \n",
    "Instead, the bisection method is a very robust method. \n",
    "\n",
    "In the function below I use \n",
    "[fsolve](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.fsolve.html),\n",
    "which is a very efficient method, as the default method, but with the possibility to switch to the brent method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def implied_volatility( price, S0, K, T, r, payoff=\"call\", method=\"fsolve\", disp=True ):\n",
    "    \"\"\" Returns Implied volatility\n",
    "        methods:  fsolve (default) or brent\n",
    "    \"\"\"\n",
    "\n",
    "    def obj_fun(vol):\n",
    "        return ( price - BS.BlackScholes(payoff=payoff, S0=S0, K=K, T=T, r=r, sigma=vol) )\n",
    "    \n",
    "    if method == \"brent\":\n",
    "        x, r = scpo.brentq( obj_fun, a=1e-15, b=500, full_output=True)\n",
    "        if r.converged == True:\n",
    "            return x\n",
    "    if method == \"fsolve\":\n",
    "        X0 = [0.1, 0.5, 1, 3]   # set of initial guess points\n",
    "        for x0 in X0:\n",
    "            x, _, solved, _ = scpo.fsolve( obj_fun, x0, full_output=True, xtol=1e-8)\n",
    "            if solved == 1:\n",
    "                return x[0]  \n",
    "    \n",
    "    if disp == True:\n",
    "        print(\"Strike\", K)\n",
    "    return -1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another approach is to find\n",
    "\n",
    "$$ \\text{argmin}_{\\theta} \\bigg( BS\\;(S, K, T, r, \\sigma) - P \\bigg)^{2n}  \\quad \\quad \\text{for } n>0$$\n",
    "\n",
    "This is an uncommon method. But it is useful when the root finder is not able to find a solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def implied_vol_minimize( price, S0, K, T, r, payoff=\"call\", disp=True ):\n",
    "    \"\"\" Returns Implied volatility by minimization\"\"\"\n",
    "    \n",
    "    n = 2     # must be even\n",
    "    def obj_fun(vol):\n",
    "        return ( BS.BlackScholes(payoff=payoff, S0=S0, K=K, T=T, r=r, sigma=vol) - price )**n\n",
    "        \n",
    "    res = scpo.minimize_scalar( obj_fun, bounds=(1e-15, 8), method='bounded')\n",
    "    if res.success == True:\n",
    "        return res.x       \n",
    "    if disp == True:\n",
    "        print(\"Strike\", K)\n",
    "    return -1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us compute the implied volatilities from the prices obtained before. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "IV_BS = []; IV_VG = []; IV_Mert = []; IV_Hest = []\n",
    "for i in range(len(strikes)):\n",
    "    IV_BS.append(implied_volatility( BS_prices[i], S0=100, K=strikes[i], T=T, r=0.1 ) )\n",
    "    IV_VG.append(implied_volatility( VG_prices[i], S0=100, K=strikes[i], T=T, r=0.1 ) )\n",
    "    IV_Mert.append(implied_volatility( Mert_prices[i], S0=100, K=strikes[i], T=T, r=0.1 ) )\n",
    "    IV_Hest.append(implied_volatility( Hest_prices[i], S0=100, K=strikes[i], T=T, r=0.1 ) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "IV_BS_m = []; IV_VG_m = []; IV_Mert_m = []; IV_Hest_m = []\n",
    "for i in range(len(strikes)):\n",
    "    IV_BS_m.append(implied_vol_minimize( BS_prices[i], S0=100, K=strikes[i], T=T, r=0.1 ) )\n",
    "    IV_VG_m.append(implied_vol_minimize( VG_prices[i], S0=100, K=strikes[i], T=T, r=0.1 ) )\n",
    "    IV_Mert_m.append(implied_vol_minimize( Mert_prices[i], S0=100, K=strikes[i], T=T, r=0.1 ) )\n",
    "    IV_Hest_m.append(implied_vol_minimize( Hest_prices[i], S0=100, K=strikes[i], T=T, r=0.1 ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see if `implied_volatility` and `implied_vol_minimize` produce the same output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Are the IV values obtained by the methods above equal?  True\n"
     ]
    }
   ],
   "source": [
    "print(\" Are the IV values obtained by the methods above equal? \", \n",
    "      np.allclose(np.array(IV_BS), np.array(IV_BS_m)) & np.allclose(np.array(IV_VG), np.array(IV_VG_m)) & \\\n",
    "np.allclose(np.array(IV_Mert), np.array(IV_Mert_m)) & np.allclose(np.array(IV_Hest), np.array(IV_Hest_m)) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,4))\n",
    "ax1 = fig.add_subplot(121); ax2 = fig.add_subplot(122)\n",
    "ax1.plot(strikes, BS_prices, label=\"BS\"); ax1.plot(strikes, VG_prices, label=\"VG\"); \n",
    "ax1.set_xlim([80,150]);ax1.set_ylim([0,30]) \n",
    "ax1.plot(strikes, Mert_prices, label=\"Mert\"); ax1.plot(strikes, Hest_prices, label=\"Hest\")\n",
    "ax1.set_title(\"Comparison of prices\"); ax1.set_xlabel(\"Strike\"); ax1.set_ylabel(\"Price\")\n",
    "ax2.plot(strikes, IV_BS, label=\"BS\"); ax2.plot(strikes, IV_VG, label=\"VG\")\n",
    "ax2.plot(strikes, IV_Mert, label=\"Mert\"); ax2.plot(strikes, IV_Hest, label=\"Hest\")\n",
    "ax2.set_title(\"Comparison of Implied volatilities\"); ax2.set_xlabel(\"Strike\"); ax2.set_ylabel(\"Imp Vol\")\n",
    "ax1.legend(); ax2.legend(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Nice plot!  We verified that the Heston, Variance Gamma and Merton models produce a smile!!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec1.2'></a>\n",
    "##  Lewis representation\n",
    "\n",
    "\n",
    "In [2], Gatheral suggests an elegant implicit expression for computing the implied volatility (Eq 5.7 page 60) generated by a stocastic process with characteristic function $\\phi_T$.     \n",
    "The expression makes use of the Lewis representation for the option price, that I presented in the notebook **1.4**. This version looks slightly different from Eq. 5.7 in [2], but they are equivalent. \n",
    "\n",
    "The value of $\\sigma$ can be obtained implicitly from \n",
    "\n",
    "$$ 0 = \\int_{0}^{\\infty} Re \\biggl[ e^{iuk} \\bigg( \\phi_T \\big(u-\\frac{i}{2} \\big) - \\phi^{BS}_T \\big(u-\\frac{i}{2} \\big) \\bigg) \\biggr] \\; \\frac{1}{u^2 + \\frac{1}{4}} du. $$\n",
    "\n",
    "Replacing $\\phi^{BS}_T(u) = e^{i(r-\\frac{1}{2}\\sigma^2) u T - \\frac{1}{2} \\sigma^2 u^2 T}$: \n",
    "\n",
    "$$ 0 = \\int_{0}^{\\infty} Re \\biggl[ e^{iuk} \\bigg( \\phi_T \\big(u-\\frac{i}{2} \\big) - \n",
    "e^{iurT} \\, e^{\\frac{1}{2}rT} \\, e^{-\\frac{1}{2}(u^2+\\frac{1}{4})\\sigma^2 T}\n",
    "\\bigg) \\biggr] \\; \\frac{1}{u^2 + \\frac{1}{4}} du. $$\n",
    "\n",
    "The implementation of `IV_Lewis` is [here](./functions/FFT.py)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "IV_L_BS = []; IV_L_VG = []; IV_L_Mert = []; IV_L_Hest = []\n",
    "for K in strikes:\n",
    "    BS.K = K; VG.K = K; Mert.K = K; Hest.K = K\n",
    "    IV_L_BS.append( BS.IV_Lewis() )\n",
    "    IV_L_VG.append( VG.IV_Lewis() )\n",
    "    IV_L_Mert.append( Mert.IV_Lewis() )\n",
    "    IV_L_Hest.append( Hest.IV_Lewis() )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(15,4))\n",
    "plt.plot(strikes, IV_BS, label=\"BS\"); plt.plot(strikes, IV_VG, label=\"VG\")\n",
    "plt.plot(strikes, IV_Mert, label=\"Mert\"); plt.plot(strikes, IV_Hest, label=\"Hest\")\n",
    "plt.plot(strikes, IV_L_BS, 'd', label=\"BS Lewis\"); plt.plot(strikes, IV_L_VG, 'd', label=\"VG Lewis\")\n",
    "plt.plot(strikes, IV_L_Mert, 'd', label=\"Mert Lewis\"); plt.plot(strikes, IV_L_Hest, 'd', label=\"Hest Lewis\")\n",
    "plt.ylim([0.08, 0.45])\n",
    "plt.legend(loc=\"upper center\"); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok, this method seems a bit slower than the previous, but it can be a good alternative."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec2'></a>\n",
    "# Market data\n",
    "\n",
    "\n",
    "Let's analyze some options market data (the expiration dates were chosen at random). I took the following values from [barchart](https://www.barchart.com/etfs-funds/quotes/SPY/options?moneyness=allRows&expiration=2020-05-15-m).\n",
    "\n",
    "The current date is 02 July 2020.\n",
    "\n",
    "- Maturity date: 10 Aug 2020  $ \\quad \\quad \\sim$ 1 week time to maturity.\n",
    "- Maturity date: 15 Jan 2021  $\\quad \\quad \\sim$ 1/2 year time to maturity\n",
    "\n",
    "This is a set of option prices written on the [SPY](https://en.wikipedia.org/wiki/SPDR_S%26P_500_Trust_ETF) ETF. \n",
    "    \n",
    "If we assume 252 business days, the time to maturity to the 10th of July corresponds to the year fraction \n",
    "$T = 5/252$, where 3, 4, and 5 July are holidays.     \n",
    "For the 6 months maturity I'm using the Act-365 convention with $T=197/365$. Counting the year fraction considering only business days it is more common when dealing with options (see [4]) but in this case I have no idea how many holidays there are till the 15th of January. \n",
    "\n",
    "The current value of SPY is $S_0 = 312.23$.    \n",
    "\n",
    "I didn't check the actual interest rate, and I will use a reasonable ad-hoc value. **This choice has a very important effect on the values of implied volatility.** In a serious analysis you should use the correct value of $r$ (which has a term structure dependent on T as well).\n",
    "\n",
    "##### Comment:\n",
    "For for very short times to maturity ($\\sim$ days), it is very difficult to replicate the smile in the ITM and OTM regions. The reasons are several. There can be numerical error issues in the pricing and in the calibration process. Or more simply, the chosen stochastic model is not so good."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Files in the data folder:  ['spy-options-exp-2021-01-15-weekly-show-all-stacked-07-05-2020.csv', 'spy-options-exp-2020-07-10-weekly-show-all-stacked-07-05-2020.csv', 'historical_data.csv']\n"
     ]
    }
   ],
   "source": [
    "files = os.listdir(os.getcwd() + \"/data\")\n",
    "print(\"Files in the data folder: \", files)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec2.1'></a>\n",
    "## 1 week maturity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "S0 = 312.23\n",
    "r = 0.05  \n",
    "T = 5/252\n",
    "opt_param = Option_param(S0=S0, K=S0, T=T, v0=0.04, exercise=\"European\", payoff=\"call\" )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Strike</th>\n",
       "      <th>Bid</th>\n",
       "      <th>Midpoint</th>\n",
       "      <th>Ask</th>\n",
       "      <th>IV</th>\n",
       "      <th>Type</th>\n",
       "      <th>Spread</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>225</th>\n",
       "      <td>370</td>\n",
       "      <td>56.89</td>\n",
       "      <td>57.11</td>\n",
       "      <td>57.33</td>\n",
       "      <td>0.1387</td>\n",
       "      <td>Put</td>\n",
       "      <td>0.44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>226</th>\n",
       "      <td>375</td>\n",
       "      <td>61.90</td>\n",
       "      <td>62.11</td>\n",
       "      <td>62.33</td>\n",
       "      <td>0.0025</td>\n",
       "      <td>Put</td>\n",
       "      <td>0.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>227</th>\n",
       "      <td>380</td>\n",
       "      <td>66.89</td>\n",
       "      <td>67.11</td>\n",
       "      <td>67.33</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>Put</td>\n",
       "      <td>0.44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>228</th>\n",
       "      <td>385</td>\n",
       "      <td>71.90</td>\n",
       "      <td>72.12</td>\n",
       "      <td>72.33</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>Put</td>\n",
       "      <td>0.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>229</th>\n",
       "      <td>390</td>\n",
       "      <td>76.88</td>\n",
       "      <td>77.10</td>\n",
       "      <td>77.33</td>\n",
       "      <td>0.7404</td>\n",
       "      <td>Put</td>\n",
       "      <td>0.45</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Strike    Bid  Midpoint    Ask      IV Type  Spread\n",
       "225     370  56.89     57.11  57.33  0.1387  Put    0.44\n",
       "226     375  61.90     62.11  62.33  0.0025  Put    0.43\n",
       "227     380  66.89     67.11  67.33  0.0000  Put    0.44\n",
       "228     385  71.90     72.12  72.33  0.0000  Put    0.43\n",
       "229     390  76.88     77.10  77.33  0.7404  Put    0.45"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "filename = \"data/\" + \"spy-options-exp-2020-07-10-weekly-show-all-stacked-07-05-2020.csv\"\n",
    "data = pd.read_csv(filename, usecols=[0,3,4,5,8,11])  \n",
    "data[\"IV\"] = data[\"IV\"].str.rstrip('%').astype('float') / 100.0   # transforms the percentage into decimal\n",
    "data[\"Spread\"] = (data.Ask - data.Bid)   # spread column\n",
    "data.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "CALL = data[data.Type==\"Call\"]\n",
    "PUT = data[data.Type==\"Put\"].reset_index(drop=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Let us recover the implied volatility from option prices.\n",
    "\n",
    "We can check if the volatilities we computed correspond to the volatilities provided in the CSV file.    \n",
    "For this purpose, we consider the Mid-price defined as the average between Bid and Ask prices. The error interval is the interval between Bid IV and Ask IV.\n",
    "\n",
    "When working with this type of data, frequently happens that the CSV file contains unreliable values of IV:\n",
    "1. because the solver was not able to converge.\n",
    "2. because other operational errors.\n",
    "\n",
    "Sometimes the problem is just the choice of using the Mid-price. Choosing another value between the Ask and the Bid price can yield a reliable value of the IV. In this case we can use `implied_vol_minimize`, which is able to reduce the error introduced by using the wrong price.     \n",
    "In other cases, the error cannot be reduced and I think it is better to ignore those values."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plots. Minimization:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "IV_call = CALL.apply(lambda x: implied_vol_minimize(x['Midpoint'], S0, x['Strike'], T, r, payoff=\"call\"), \n",
    "               axis=1)\n",
    "CALL = CALL.assign(IV_mid=IV_call.values)\n",
    "IV_put = PUT.apply(lambda x: implied_vol_minimize(x['Midpoint'], S0, x['Strike'], T, r, payoff=\"put\", \n",
    "                                                  disp=False), axis=1)\n",
    "PUT = PUT.assign(IV_mid=IV_put.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1224x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(17,4))\n",
    "ax1 = fig.add_subplot(131); ax2 = fig.add_subplot(132); ax3 = fig.add_subplot(133)\n",
    "ax1.plot(CALL.Strike, CALL.Midpoint, '-', label=\"CALL\")\n",
    "ax1.plot(PUT.Strike, PUT.Midpoint, '-', label=\"PUT\")\n",
    "ax2.plot(CALL.Strike, CALL.IV_mid, '.', label=\"BS inversion\")\n",
    "ax2.plot(CALL.Strike, CALL.IV, '.', label=\"provided vol\")\n",
    "ax3.plot(PUT.Strike, PUT.IV_mid,'.', label=\"BS inversion\")\n",
    "ax3.plot(PUT.Strike, PUT.IV, '.', label=\"provided vol\")\n",
    "ax1.set_title(\"Price curve\"); ax2.set_title(\"CALL Volatility smile\"); ax3.set_title(\"PUT Volatility smile\")\n",
    "ax1.set_xlabel(\"strike\"); ax2.set_xlabel(\"strike\"); ax3.set_xlabel(\"strike\")\n",
    "ax1.legend(); ax2.legend(); ax3.legend(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plots. Root finder:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "IV_call = CALL.apply(lambda x: implied_volatility(x['Midpoint'], S0, x['Strike'], T, r, payoff=\"call\", \n",
    "                                                  disp=False), axis=1)\n",
    "CALL = CALL.assign(IV_mid=IV_call.values)\n",
    "IV_put = PUT.apply(lambda x: implied_volatility(x['Midpoint'], S0, x['Strike'], T, r, payoff=\"put\", disp=False),\n",
    "                  axis=1)\n",
    "PUT = PUT.assign(IV_mid=IV_put.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1224x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(17,4))\n",
    "ax1 = fig.add_subplot(131); ax2 = fig.add_subplot(132); ax3 = fig.add_subplot(133)\n",
    "ax1.plot(CALL.Strike, CALL.Midpoint, '-', label=\"CALL\")\n",
    "ax1.plot(PUT.Strike, PUT.Midpoint, '-', label=\"PUT\")\n",
    "ax2.plot(CALL[CALL.IV_mid != -1].Strike, CALL[CALL.IV_mid != -1].IV_mid, '.', label=\"BS inversion\")\n",
    "ax2.plot(CALL.Strike, CALL.IV, '.', label=\"provided vol\")\n",
    "ax2.plot(CALL[CALL.IV_mid == -1].Strike, CALL[CALL.IV_mid == -1].IV_mid, '.', label=\"inconsistent values\")\n",
    "ax3.plot(PUT[PUT.IV_mid != -1].Strike, PUT[PUT.IV_mid != -1].IV_mid,'.', label=\"BS inversion\")\n",
    "ax3.plot(PUT.Strike, PUT.IV, '.', label=\"provided vol\")\n",
    "ax3.plot(PUT[PUT.IV_mid == -1].Strike, PUT[PUT.IV_mid == -1].IV_mid,'.', label=\"inconsistent values\")\n",
    "ax1.set_title(\"Price curve\"); ax2.set_title(\"CALL Volatility smile\"); ax3.set_title(\"PUT Volatility smile\")\n",
    "ax1.set_xlabel(\"strike\"); ax2.set_xlabel(\"strike\"); ax3.set_xlabel(\"strike\")\n",
    "ax1.legend(); ax2.legend(); ax3.legend(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Inconsistent values:** when there is no implied volatility able to reproduce the mid-price, the `implied_volatility` function returns $-1$.  \n",
    "\n",
    "Using `implied_vol_minimize` provide values for the put option that `implied_volatility` was not able to retrieve. However, it is difficult to say if these values are reliable or not.\n",
    "\n",
    "Let use ignore the data point with $IV = -1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "CALL = CALL[CALL.IV_mid != -1].reset_index(drop=True)\n",
    "PUT = PUT[PUT.IV_mid != -1].reset_index(drop=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calibration\n",
    "\n",
    "If we call $\\Theta$ the set of parameters, the goal is to find the optimal parameters $\\Theta^*$ that minimize the following objective function:\n",
    "\n",
    "$$ \\sum_{i=1}^{N} w_i \\biggl( P_i - f(K_i|\\Theta) \\biggr)^2 $$\n",
    "\n",
    "where $P_i$ are the market prices, $f$ is the pricing function and $w_i$ are weights usually defined as \n",
    "\n",
    "$$ w_i = \\frac{1}{\\text{spread}_i} $$\n",
    "\n",
    "(they give more importance to the points with smaller spread).\n",
    "\n",
    "Among the many numerical methods, here I use the following:\n",
    "- [curve_fit](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html)\n",
    "    It uses the `trf` method when the parameters are bounded and the `Levemberg-Marquadt` method for unbounded parameters.\n",
    "- [minimize(method=’SLSQP’)](https://docs.scipy.org/doc/scipy/reference/optimize.minimize-slsqp.html#optimize-minimize-slsqp)\n",
    "\n",
    "For the unconstrained problem (Heston, Merton and VG) I use `curve_fit`, while for the constrained Heston problem I use `minimize`.\n",
    "\n",
    "##### Comment:\n",
    "In order to make the code simpler, I will only use CALL prices for the calibration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "option_type = CALL\n",
    "prices = option_type.Midpoint.values\n",
    "strikes = option_type.Strike.values\n",
    "spreads = option_type.Spread.values\n",
    "payoff = \"call\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Merton parameters calibration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f_Mert(x, sig, lam, muJ, sigJ):\n",
    "    Merton_param = Merton_process(r=r, sig=sig, lam=lam, muJ=muJ, sigJ=sigJ)\n",
    "    opt_param = Option_param(S0=S0, K=x, T=T, v0=0.04, exercise=\"European\", payoff=\"call\" )\n",
    "    Mert = Merton_pricer(opt_param, Merton_param)\n",
    "    return Mert.closed_formula()\n",
    "\n",
    "init_vals = [0.2, 1, -0.5, 0.2]\n",
    "bounds=( [0, 0, -np.inf, 0], [2, np.inf, 5, 5] )\n",
    "params_Mert = scpo.curve_fit(f_Mert, strikes, prices, p0=init_vals, bounds=bounds, sigma=spreads) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### VG parameters calibration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f_VG(x, theta, sigma, kappa):\n",
    "    VG_param = VG_process(r=r, theta=theta, sigma=sigma, kappa=kappa)\n",
    "    opt_param = Option_param(S0=S0, K=K, T=T, v0=0.04, exercise=\"European\", payoff=\"call\" )\n",
    "    VG = VG_pricer(opt_param, VG_param)\n",
    "    return VG.FFT(x)\n",
    "\n",
    "init_vals = [-0.05, 0.2, 0.1]\n",
    "bounds=( [-np.inf, 0, 0], [np.inf, 5, np.inf] )\n",
    "params_VG = scpo.curve_fit(f_VG, strikes, prices, p0=init_vals, bounds=bounds, sigma=spreads) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Heston parameters calibration\n",
    "\n",
    "What to do with the **Feller condition**?\n",
    "\n",
    "The Feller condition is hardly satisfied in the market, mainly because having $\\kappa \\theta > \\frac{1}{2} \\sigma^2$ implies a high mean reversion which reduces the volatility of the stochastic volatility $\\sigma^2$.    \n",
    "The vol of vol is responsible for the convexity of the smile. \n",
    "In order to increase the convexity to match the empirical smile, we have to increase $\\sigma^2$ violating the Feller condition.   \n",
    "However this is not really an issue, at the moment the $v_t$ reaches $0$ we have a positive drift $dv_t = \\kappa \\theta dt$ that will push instantly the process away from 0.\n",
    "\n",
    "Let us calibrate the two cases:\n",
    "- Ignoring the Feller condition (using `curve_fit`).\n",
    "- Introducing the Feller condition as an inequality constraint (using `minimize`).\n",
    "\n",
    "#### Comment:\n",
    "1. The calibration of the Heston pricing model is a difficult task and here I'm adopting a very naive approach.    \n",
    "For more information I suggest you look at [3] where the problem is treated rigorously and there is also a literature review. \n",
    "\n",
    "2. The calibration of 5 parameters will make the following code **quite slow**. \n",
    "In [3] there are several suggestions to speed up the code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Unconstrained problem\n",
    "def f_Hest(x, rho, sigma, theta, kappa, v0):\n",
    "    Heston_param = Heston_process(mu=r, rho=rho, sigma=sigma, theta=theta, kappa=kappa)\n",
    "    opt_param = Option_param(S0=S0, K=K, T=T, v0=v0, exercise=\"European\", payoff=payoff )\n",
    "    Hest = Heston_pricer(opt_param, Heston_param)\n",
    "    return Hest.FFT(x)\n",
    "\n",
    "init_vals = [-0.6, 1.0, 0.04, 2.5, 0.04]\n",
    "bounds=( [-1, 1e-15, 1e-15, 1e-15, 1e-15], [1, np.inf, 2, np.inf, 2] )\n",
    "params_Hest = scpo.curve_fit(f_Hest, strikes, prices, p0=init_vals, bounds=bounds, sigma=spreads,\n",
    "                            xtol=1e-4, max_nfev=1000) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n"
     ]
    }
   ],
   "source": [
    "## Constrained problem\n",
    "init_vals = [-0.4, 1.1, 0.1, 0.6, 0.02]  # rho, sigma, theta, kappa, v0\n",
    "#init_vals = [-0.7, 2.8, 0.7, 0.1, 0.02]  # alternative starting point\n",
    "\n",
    "# bounds and constraint\n",
    "bounds = ( (-1,1), (1e-15,np.inf), (1e-15, 50), (1e-15, 50), (1e-15, 10) )\n",
    "\n",
    "def Feller(x):\n",
    "    \"\"\" Feller condition \"\"\"\n",
    "    return 2*x[3] * x[2] - x[1]**2 - 1e-6\n",
    "cons = ({\"fun\": Feller, \"type\": \"ineq\"})           # inequality constraint\n",
    "\n",
    "def least_sq(x, prices, strikes, spread):\n",
    "    \"\"\" Objective function \"\"\"\n",
    "    Heston_param = Heston_process(mu=r, rho=x[0], sigma=x[1], theta=x[2], kappa=x[3])\n",
    "    opt_param = Option_param(S0=S0, K=K, T=T, v0=x[4], exercise=\"European\", payoff=\"call\" )\n",
    "    Hest = Heston_pricer(opt_param, Heston_param)\n",
    "    prices_calib = Hest.FFT(strikes)\n",
    "    return np.sum( ((prices_calib - prices)/spread)**2 ) \n",
    "    \n",
    "result = scpo.minimize(least_sq, x0=init_vals, args=(prices, strikes, spreads),\n",
    "                  method='SLSQP', bounds=bounds,\n",
    "                  constraints=cons, tol=1e-4, options={\"maxiter\":500})\n",
    "print(result.message)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Now we can price the options using the just calibrated parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "opt_param_Feller = Option_param(S0=S0, K=K, T=T, v0=result.x[4], exercise=\"European\", payoff=payoff )\n",
    "opt_param = Option_param(S0=S0, K=K, T=T, v0=params_Hest[0][4], exercise=\"European\", payoff=payoff )\n",
    "\n",
    "Merton_param = Merton_process(r=r, sig=params_Mert[0][0], lam=params_Mert[0][1], \n",
    "                              muJ=params_Mert[0][2], sigJ=params_Mert[0][3])\n",
    "Mert = Merton_pricer(opt_param, Merton_param)\n",
    "VG_param = VG_process(r=r, theta=params_VG[0][0], sigma=params_VG[0][1], kappa=params_VG[0][2])\n",
    "VG = VG_pricer(opt_param, VG_param)\n",
    "Heston_param_Feller = Heston_process(mu=r, rho=result.x[0], sigma=result.x[1], \n",
    "                                     theta=result.x[2], kappa=result.x[3])\n",
    "Heston_param = Heston_process(mu=r, rho=params_Hest[0][0], sigma=params_Hest[0][1], theta=params_Hest[0][2], \n",
    "                              kappa=params_Hest[0][3])\n",
    "Hest = Heston_pricer(opt_param, Heston_param)\n",
    "Hest_Feller = Heston_pricer(opt_param_Feller, Heston_param_Feller)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "Mert_pred = Mert.FFT(strikes)          # \"pred\" stays for \"predicted\"\n",
    "VG_pred = VG.FFT(strikes)\n",
    "Hest_pred = Hest.FFT(strikes)\n",
    "Hest_Feller_pred = Hest_Feller.FFT(strikes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1224x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(17,4))\n",
    "ax1 = fig.add_subplot(131); ax2 = fig.add_subplot(132); ax3 = fig.add_subplot(133)\n",
    "ax1.plot(strikes, prices,'.', label=\"midpoint\")\n",
    "ax2.plot(strikes, prices,'.', label=\"midpoint\")\n",
    "ax3.plot(strikes, prices,'.', label=\"midpoint\")\n",
    "ax1.plot(strikes, Mert_pred, label=\"Merton\")\n",
    "ax2.plot(strikes, VG_pred, label=\"VG\")\n",
    "ax3.plot(strikes, Hest_pred, label=\"Heston\")\n",
    "ax3.plot(strikes, Hest_Feller_pred, label=\"Heston with Feller cond.\")\n",
    "ax1.set_title(\"Merton model\"); ax2.set_title(\"VG model\"); ax3.set_title(\"Heston model\")\n",
    "ax1.set_xlabel(\"strike\"); ax2.set_xlabel(\"strike\"); ax3.set_xlabel(\"strike\")\n",
    "ax1.legend(); ax2.legend(); ax3.legend(); plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Are the values sorted? Merton:  True\n",
      "Are the values sorted? VG:  False\n",
      "Are the values sorted? Heston:  True\n",
      "Are the values sorted? Heston Feller:  True\n",
      "Negative values? ['VG', 'Hest Feller']\n"
     ]
    }
   ],
   "source": [
    "print(\"Are the values sorted? Merton: \", (np.diff(Mert_pred)<=0).all() if payoff==\"call\" \n",
    "      else (np.diff(Mert_pred)>=0).all() )\n",
    "print(\"Are the values sorted? VG: \", (np.diff(VG_pred)<=0).all() if payoff==\"call\" \n",
    "      else (np.diff(VG_pred)>=0).all() )\n",
    "print(\"Are the values sorted? Heston: \", (np.diff(Hest_pred)<=0).all() if payoff==\"call\" \n",
    "      else (np.diff(Hest_pred)>=0).all() )\n",
    "print(\"Are the values sorted? Heston Feller: \", (np.diff(Hest_Feller_pred)<=0).all() if payoff==\"call\" \n",
    "      else (np.diff(Hest_Feller_pred)>=0).all() )\n",
    "temp_list = list(compress([\"VG\", \"Mert\", \"Hest\", \"Hest Feller\"],\n",
    "                [(VG_pred<0).any(), (Mert_pred<0).any(), (Hest_pred<0).any(), (Hest_Feller_pred<0).any()]) )\n",
    "print(\"Negative values?\", temp_list if len(temp_list)!=0 else \"No\" ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As already explained, the FFT method has problems for deep OTM values and short maturities. \n",
    "We can replace manually the negative values with fake values (we don't care too much about values with magnitude $\\sim 10^{-8}$). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "Hest_Feller_pred[Hest_Feller_pred<0] = 1e-8\n",
    "VG_pred[VG_pred<0] = 1e-8"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us compare the errors of the used pricing models!\n",
    "\n",
    "I choose MAV instead of MSE because I am only interested in the mean distance between the market price and the model price."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Merton. Mean absolute error:  0.16439607355767683\n",
      "VG. Mean absolute error:  0.20894423405010518\n",
      "Heston. Mean absolute error:  0.17674185214553964\n",
      "Heston with Feller. Mean absolute error:  0.2253856273769932\n"
     ]
    }
   ],
   "source": [
    "print(\"Merton. Mean absolute error: \", np.abs( prices - Mert_pred ).mean() )\n",
    "print(\"VG. Mean absolute error: \", np.abs( prices - VG_pred ).mean() )\n",
    "print(\"Heston. Mean absolute error: \",np.abs( prices - Hest_pred ).mean() )\n",
    "print(\"Heston with Feller. Mean absolute error: \",np.abs( prices - Hest_Feller_pred ).mean() )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Merton and Heston are the best, while the Heston with Feller condition is the worst."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(strikes, spreads, label=\"Spread\", linewidth=3, color=\"red\")\n",
    "plt.plot(strikes, np.abs( prices - Hest_pred ), label=\"Hest\")\n",
    "plt.plot(strikes, np.abs( prices - Hest_Feller_pred ), label=\"Hest with Feller\")\n",
    "plt.plot(strikes, np.abs( prices - Mert_pred ), label=\"Mert\")\n",
    "plt.plot(strikes, np.abs( prices - VG_pred ), label=\"VG\")\n",
    "plt.title(\"Pricing errors\"); plt.legend(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Implied volatility smile generated by the pricing models!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "IV_VG = []; IV_Mert = []; IV_Hest = []; IV_Hest_F = []\n",
    "for i,K in enumerate(strikes):\n",
    "    IV_VG.append(implied_vol_minimize( VG_pred[i], S0=S0, K=K, T=T, r=r ) )\n",
    "    IV_Mert.append(implied_vol_minimize( Mert_pred[i], S0=S0, K=K, T=T, r=r ) )\n",
    "    IV_Hest.append(implied_vol_minimize( Hest_pred[i], S0=S0, K=K, T=T, r=r ) )\n",
    "    IV_Hest_F.append(implied_vol_minimize( Hest_Feller_pred[i], S0=S0, K=K, T=T, r=r ) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,4))\n",
    "ax1 = fig.add_subplot(121); ax2 = fig.add_subplot(122)\n",
    "ax1.plot(strikes, option_type.IV_mid, '.', label=\"BS inversion\")\n",
    "ax2.plot(strikes, option_type.IV_mid, '.', label=\"BS inversion\")\n",
    "ax1.plot(strikes, IV_VG, label=\"VG\"); ax2.plot(strikes, IV_VG, label=\"VG\")\n",
    "ax1.plot(strikes, IV_Mert, label=\"Mert\"); ax2.plot(strikes, IV_Mert, label=\"Mert\") \n",
    "ax1.plot(strikes, IV_Hest, label=\"Hest\"); ax2.plot(strikes, IV_Hest, label=\"Hest\")\n",
    "ax1.plot(strikes, IV_Hest_F, label=\"Hest Feller\"); ax2.plot(strikes, IV_Hest_F, label=\"Hest Feller\")\n",
    "ax2.axis([290,350,0.14,0.4]); ax2.axvline(S0, color=\"black\", label=\"ATM\", linewidth=1)\n",
    "ax2.set_title(\"Model Implied volatilities. ATM Zoom\"); ax1.set_xlabel(\"Strike\"); ax1.set_ylabel(\"Imp Vol\")\n",
    "ax1.set_title(\"Model Implied volatilities\"); ax2.set_xlabel(\"Strike\"); ax2.set_ylabel(\"Imp Vol\")\n",
    "ax1.legend(); ax2.legend(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The pricing models produce a good fit in the neighborhood of the ATM region.\n",
    "\n",
    "In this region, the Merton model is the best.\n",
    "\n",
    "#### Comment:\n",
    "As expected the Heston model with NO Feller condition provides much better results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec2.2'></a>\n",
    "# 6 months maturity\n",
    "\n",
    "\n",
    "Now let's go over the steps taken before and calculate the volatility smile for options with a maturity of 6 months.\n",
    "\n",
    "Sorry. The code will be a little repetitive."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "S0 = 312.23\n",
    "r = 0.015\n",
    "T = 197/365  \n",
    "opt_param = Option_param(S0=S0, K=S0, T=T, v0=0.04, exercise=\"European\", payoff=\"call\" )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Strike</th>\n",
       "      <th>Bid</th>\n",
       "      <th>Midpoint</th>\n",
       "      <th>Ask</th>\n",
       "      <th>IV</th>\n",
       "      <th>Type</th>\n",
       "      <th>Spread</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>499</th>\n",
       "      <td>535</td>\n",
       "      <td>223.36</td>\n",
       "      <td>223.98</td>\n",
       "      <td>224.59</td>\n",
       "      <td>0.5099</td>\n",
       "      <td>Put</td>\n",
       "      <td>1.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>500</th>\n",
       "      <td>540</td>\n",
       "      <td>228.35</td>\n",
       "      <td>228.97</td>\n",
       "      <td>229.58</td>\n",
       "      <td>0.5168</td>\n",
       "      <td>Put</td>\n",
       "      <td>1.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>501</th>\n",
       "      <td>545</td>\n",
       "      <td>233.33</td>\n",
       "      <td>233.95</td>\n",
       "      <td>234.56</td>\n",
       "      <td>0.5233</td>\n",
       "      <td>Put</td>\n",
       "      <td>1.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>502</th>\n",
       "      <td>550</td>\n",
       "      <td>238.32</td>\n",
       "      <td>238.94</td>\n",
       "      <td>239.55</td>\n",
       "      <td>0.5301</td>\n",
       "      <td>Put</td>\n",
       "      <td>1.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>503</th>\n",
       "      <td>555</td>\n",
       "      <td>243.31</td>\n",
       "      <td>243.93</td>\n",
       "      <td>244.54</td>\n",
       "      <td>0.5368</td>\n",
       "      <td>Put</td>\n",
       "      <td>1.23</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Strike     Bid  Midpoint     Ask      IV Type  Spread\n",
       "499     535  223.36    223.98  224.59  0.5099  Put    1.23\n",
       "500     540  228.35    228.97  229.58  0.5168  Put    1.23\n",
       "501     545  233.33    233.95  234.56  0.5233  Put    1.23\n",
       "502     550  238.32    238.94  239.55  0.5301  Put    1.23\n",
       "503     555  243.31    243.93  244.54  0.5368  Put    1.23"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "filename = \"data/\" + \"spy-options-exp-2021-01-15-weekly-show-all-stacked-07-05-2020.csv\"\n",
    "data = pd.read_csv(filename, usecols=[1,4,5,6,9,12])\n",
    "data[\"IV\"] = data[\"IV\"].str.rstrip('%').astype('float') / 100.0   # transforms the percentage into decimal\n",
    "data[\"Spread\"] = (data.Ask - data.Bid)   # spread column\n",
    "data.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "CALL = data[data.Type==\"Call\"]\n",
    "PUT = data[data.Type==\"Put\"].reset_index(drop=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plots, root finder:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "IV_call = CALL.apply(lambda x: implied_volatility(x['Midpoint'], S0, x['Strike'], T, r, payoff=\"call\", \n",
    "                                                  disp=False), axis=1)\n",
    "CALL = CALL.assign(IV_mid=IV_call.values)\n",
    "IV_put = PUT.apply(lambda x: implied_volatility(x['Midpoint'], S0, x['Strike'], T, r, payoff=\"put\", disp=False),\n",
    "                  axis=1)\n",
    "PUT = PUT.assign(IV_mid=IV_put.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1224x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(17,4))\n",
    "ax1 = fig.add_subplot(131); ax2 = fig.add_subplot(132); ax3 = fig.add_subplot(133)\n",
    "ax1.plot(CALL.Strike, CALL.Midpoint, '-', label=\"CALL\")\n",
    "ax1.plot(PUT.Strike, PUT.Midpoint, '-', label=\"PUT\")\n",
    "ax2.plot(CALL[CALL.IV_mid != -1].Strike, CALL[CALL.IV_mid != -1].IV_mid, '.', label=\"BS inversion\")\n",
    "ax2.plot(CALL.Strike, CALL.IV, '.', label=\"provided vol\")\n",
    "ax2.plot(CALL[CALL.IV_mid == -1].Strike, CALL[CALL.IV_mid == -1].IV_mid, '.', label=\"inconsistent values\")\n",
    "ax3.plot(PUT[PUT.IV_mid != -1].Strike, PUT[PUT.IV_mid != -1].IV_mid,'.', label=\"BS inversion\")\n",
    "ax3.plot(PUT.Strike, PUT.IV, '.', label=\"provided vol\")\n",
    "ax3.plot(PUT[PUT.IV_mid == -1].Strike, PUT[PUT.IV_mid == -1].IV_mid,'.', label=\"inconsistent values\")\n",
    "ax1.set_title(\"Price curve\"); ax2.set_title(\"CALL Volatility smile\"); ax3.set_title(\"PUT Volatility smile\")\n",
    "ax1.set_xlabel(\"strike\"); ax2.set_xlabel(\"strike\"); ax3.set_xlabel(\"strike\")\n",
    "ax1.legend(); ax2.legend(); ax3.legend(); plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "CALL = CALL[CALL.IV_mid != -1].reset_index(drop=True)\n",
    "PUT = PUT[PUT.IV_mid != -1].reset_index(drop=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calibration\n",
    "\n",
    "Since we found that the Feller condition is not satisfied, I consider only the unconstrained problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "option_type = CALL\n",
    "prices = option_type.Midpoint.values\n",
    "strikes = option_type.Strike.values\n",
    "spreads = option_type.Spread.values\n",
    "payoff = \"call\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f_Mert(x, sig, lam, muJ, sigJ):\n",
    "    Merton_param = Merton_process(r=r, sig=sig, lam=lam, muJ=muJ, sigJ=sigJ)\n",
    "    opt_param = Option_param(S0=S0, K=x, T=T, v0=0.04, exercise=\"European\", payoff=payoff )\n",
    "    Mert = Merton_pricer(opt_param, Merton_param)\n",
    "    return Mert.closed_formula()\n",
    "\n",
    "init_vals = [0.2, 1, -0.5, 0.2]\n",
    "bounds=( [0, 0, -np.inf, 0], [2, np.inf, 5, 5] )\n",
    "params_Mert = scpo.curve_fit(f_Mert, strikes, prices, p0=init_vals, bounds=bounds, sigma=spreads) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f_VG(x, theta, sigma, kappa):\n",
    "    VG_param = VG_process(r=r, theta=theta, sigma=sigma, kappa=kappa)\n",
    "    opt_param = Option_param(S0=S0, K=K, T=T, v0=0.04, exercise=\"European\", payoff=payoff )\n",
    "    VG = VG_pricer(opt_param, VG_param)\n",
    "    return VG.FFT(x)\n",
    "\n",
    "init_vals = [-0.05, 0.2, 0.1]\n",
    "bounds=( [-np.inf, 0, 0], [np.inf, 5, np.inf] )\n",
    "params_VG = scpo.curve_fit(f_VG, strikes, prices, p0=init_vals, bounds=bounds, sigma=spreads) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f_Hest(x, rho, sigma, theta, kappa, v0):\n",
    "    Heston_param = Heston_process(mu=r, rho=rho, sigma=sigma, theta=theta, kappa=kappa)\n",
    "    opt_param = Option_param(S0=S0, K=K, T=T, v0=v0, exercise=\"European\", payoff=payoff )\n",
    "    Hest = Heston_pricer(opt_param, Heston_param)\n",
    "    return Hest.FFT(x)\n",
    "\n",
    "init_vals = [-0.6, 0.1, 0.04, 10, 0.01]\n",
    "bounds=( [-1, 1e-15, 1e-15, 1e-15, 1e-15], [1, np.inf, 2, np.inf, 2] )\n",
    "params_Hest = scpo.curve_fit(f_Hest, strikes, prices, p0=init_vals, bounds=bounds, sigma=spreads)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Now we can price the options using the just calibrated parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "opt_param = Option_param(S0=S0, K=K, T=T, v0=params_Hest[0][4], exercise=\"European\", payoff=payoff )\n",
    "Merton_param = Merton_process(r=r, sig=params_Mert[0][0], lam=params_Mert[0][1], \n",
    "                              muJ=params_Mert[0][2], sigJ=params_Mert[0][3])\n",
    "Mert = Merton_pricer(opt_param, Merton_param)\n",
    "VG_param = VG_process(r=r, theta=params_VG[0][0], sigma=params_VG[0][1], kappa=params_VG[0][2])\n",
    "VG = VG_pricer(opt_param, VG_param)\n",
    "Heston_param = Heston_process(mu=r, rho=params_Hest[0][0], sigma=params_Hest[0][1], theta=params_Hest[0][2], \n",
    "                              kappa=params_Hest[0][3])\n",
    "Hest = Heston_pricer(opt_param, Heston_param)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1224x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(17,4))\n",
    "ax1 = fig.add_subplot(131); ax2 = fig.add_subplot(132); ax3 = fig.add_subplot(133)\n",
    "ax1.plot(strikes, prices,'.', label=\"midpoint\")\n",
    "ax2.plot(strikes, prices,'.', label=\"midpoint\")\n",
    "ax3.plot(strikes, prices,'.', label=\"midpoint\")\n",
    "ax1.plot(strikes, Mert.FFT(strikes), label=\"Merton\")\n",
    "ax2.plot(strikes, VG.FFT(strikes), label=\"VG\")\n",
    "ax3.plot(strikes, Hest.FFT(strikes), label=\"Heston\")\n",
    "ax1.set_title(\"Merton model\"); ax2.set_title(\"VG model\"); ax3.set_title(\"Heston model\")\n",
    "ax1.set_xlabel(\"strike\"); ax2.set_xlabel(\"strike\"); ax3.set_xlabel(\"strike\")\n",
    "ax1.legend(); ax2.legend(); ax3.legend(); plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "Mert_pred = Mert.FFT(strikes)\n",
    "VG_pred = VG.FFT(strikes)\n",
    "Hest_pred = Hest.FFT(strikes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Are the values sorted? Mert:  True\n",
      "Are the values sorted? VG:  True\n",
      "Are the values sorted? Hest:  True\n",
      "Negative values? No\n"
     ]
    }
   ],
   "source": [
    "print(\"Are the values sorted? Mert: \", (np.diff(Mert_pred)<=0).all() if payoff==\"call\" \n",
    "      else (np.diff(Mert_pred)>=0).all() )\n",
    "print(\"Are the values sorted? VG: \", (np.diff(VG_pred)<=0).all() if payoff==\"call\" \n",
    "      else (np.diff(VG_pred)>=0).all() )\n",
    "print(\"Are the values sorted? Hest: \", (np.diff(Hest_pred)<=0).all() if payoff==\"call\" \n",
    "      else (np.diff(Hest_pred)>=0).all() )\n",
    "temp_list = list(compress([\"VG\", \"Mert\", \"Hest\"],[(VG_pred<0).any(), (Mert_pred<0).any(), (Hest_pred<0).any()]) )\n",
    "print(\"Negative values?\", temp_list if len(temp_list)!=0 else \"No\" ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Merton. Mean absolute error:  0.08542792018656539\n",
      "VG. Mean absolute error:  0.26298353895417736\n",
      "Heston. Mean absolute error:  0.29792561936921413\n"
     ]
    }
   ],
   "source": [
    "print(\"Merton. Mean absolute error: \", np.abs( prices - Mert_pred ).mean() )\n",
    "print(\"VG. Mean absolute error: \", np.abs( prices - VG_pred ).mean() )\n",
    "print(\"Heston. Mean absolute error: \",np.abs( prices - Hest_pred ).mean() )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(strikes, np.abs( prices - Hest_pred ), label=\"Hest\")\n",
    "plt.plot(strikes, np.abs( prices - Mert_pred ), label=\"Mert\")\n",
    "plt.plot(strikes, np.abs( prices - VG_pred ), label=\"VG\")\n",
    "plt.plot(strikes, spreads, label=\"Spread\", linewidth=3, color=\"red\")\n",
    "plt.title(\"Pricing errors\"); plt.legend(); plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "IV_VG = []; IV_Mert = []; IV_Hest = []\n",
    "for i,K in enumerate(CALL.Strike.values):\n",
    "    IV_VG.append(implied_vol_minimize( VG_pred[i], S0=S0, K=K, T=T, r=r ) )\n",
    "    IV_Mert.append(implied_vol_minimize( Mert_pred[i], S0=S0, K=K, T=T, r=r ) )\n",
    "    IV_Hest.append(implied_vol_minimize( Hest_pred[i], S0=S0, K=K, T=T, r=r ) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,4))\n",
    "ax1 = fig.add_subplot(121); ax2 = fig.add_subplot(122)\n",
    "ax1.plot(strikes, option_type.IV_mid, '.', label=\"BS inversion\")\n",
    "ax2.plot(strikes, option_type.IV_mid, '.', label=\"BS inversion\")\n",
    "ax1.plot(strikes, IV_VG, label=\"VG\"); ax2.plot(strikes, IV_VG, label=\"VG\")\n",
    "ax1.plot(strikes, IV_Mert, label=\"Mert\"); ax2.plot(strikes, IV_Mert, label=\"Mert\") \n",
    "ax1.plot(strikes, IV_Hest, label=\"Hest\"); ax2.plot(strikes, IV_Hest, label=\"Hest\")\n",
    "ax2.axis([250,400,0.15,0.4]); ax2.axvline(S0, color=\"black\", label=\"ATM\", linewidth=1)\n",
    "ax2.set_title(\"Model Implied volatilities. ATM Zoom\"); ax1.set_xlabel(\"Strike\"); ax1.set_ylabel(\"Imp Vol\")\n",
    "ax1.set_title(\"Model Implied volatilities\"); ax2.set_xlabel(\"Strike\"); ax2.set_ylabel(\"Imp Vol\")\n",
    "ax1.legend(); ax2.legend(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again the Merton model is the model that performs better."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "[1] Rebonato, R. (1999) \"Volatility and Correlation: In the Pricing of Equity, FX and Interest-Rate Options\", Wiley Series in Financial Engineering.\n",
    "\n",
    "[2] Gatheral, J. (2006) \"The Volatility Surface: A Practitioner’s Guide (Wiley Finance Series)\", John Wiley & Sons, New York.\n",
    "\n",
    "[3] Yiran Cui, Sebastian del Baño Rollin, Guido Germano, (2017), \"Full and fast calibration of the Heston stochastic volatility model\" European Journal of operational research. [link](http://www0.cs.ucl.ac.uk/staff/g.germano/papers/EurJOperRes_2017.pdf)\n",
    "\n",
    "[4] John Hull. \"Options, Futures, and Other Derivatives\"."
   ]
  }
 ],
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   "display_name": "Python 3",
   "language": "python",
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    "name": "ipython",
    "version": 3
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